scholarly journals Mean dynamics of transitional boundary-layer flow

2011 ◽  
Vol 682 ◽  
pp. 617-651 ◽  
Author(s):  
J. KLEWICKI ◽  
R. EBNER ◽  
X. WU
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Boundary Layer Flow ◽  
Layer Structure ◽  
Momentum Equation ◽  
Stress Profile ◽  
Transitional Regime ◽  
The Mean ◽  
Layer Flow

The dynamical mechanisms underlying the redistribution of mean momentum and vorticity are explored for transitional two-dimensional boundary-layer flow at nominally zero pressure gradient. The analyses primarily employ the direct numerical simulation database of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5), but are supplemented with verifications utilizing subsequent similar simulations. The transitional regime is taken to include both an instability stage, which effectively generates a finite Reynolds stress profile, −ρuv(y), and a nonlinear development stage, which progresses until the terms in the mean momentum equation attain the magnitude ordering of the four-layer structure revealed by Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303). Self-consistently applied criteria reveal that the third layer of this structure forms first, followed by layers IV and then II and I. For the present flows, the four-layer structure is estimated to be first realized at a momentum thickness Reynolds number Rθ = U∞ θ/ν ≃ 780. The first-principles-based theory of Fife et al. (J. Disc. Cont. Dyn. Syst. A, vol. 24, 2009, p. 781) is used to describe the mean dynamics in the laminar, transitional and four-layer regimes. As in channel flow, the transitional regime is marked by a non-negligible influence of all three terms in the mean momentum equation at essentially all positions in the boundary layer. During the transitional regime, the action of the Reynolds stress gradient rearranges the mean viscous force and mean advection profiles. This culminates with the segregation of forces characteristic of the four-layer regime. Empirical and theoretical evidence suggests that the formation of the four-layer structure also underlies the emergence of the mean dynamical properties characteristic of the high-Reynolds-number flow. These pertain to why and where the mean velocity profile increasingly exhibits logarithmic behaviour, and how and why the Reynolds stress distribution develops such that the inner normalized position of its peak value, ym+, exhibits a Reynolds number dependence according to $y_m^+ {\,\simeq\,} 1.9 \sqrt{\delta^+}$.

Effect of Reynolds number on drag reduction in turbulent boundary layer flow over liquid–gas interface

2020 ◽  
Vol 32 (12) ◽  
pp. 122111
Author(s):  
Hongyuan Li ◽  
SongSong Ji ◽  
Xiangkui Tan ◽  
Zexiang Li ◽  
Yaolei Xiang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Boundary Layer Flow ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

2008 ◽  
Vol 614 ◽  
pp. 315-327 ◽  
Author(s):  
UWE EHRENSTEIN ◽  
FRANÇOIS GALLAIRE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Perturbation Analysis ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Layer Flow

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

scholarly journals Mean dynamics of transitional channel flow

2011 ◽  
Vol 678 ◽  
pp. 451-481 ◽  
Author(s):  
J. ELSNAB ◽  
J. KLEWICKI ◽  
D. MAYNES ◽  
T. AMEEL
Keyword(s):  
Reynolds Number ◽  
Reynolds Stress ◽  
Channel Flow ◽  
Inflection Point ◽  
Stress Gradient ◽  
Development Stage ◽  
Stress Profile ◽  
Turbulent Regime ◽  
Nonlinear Development ◽  
The Mean

The redistribution of mean momentum and vorticity, along with the mechanisms underlying these redistribution processes, is explored for post-laminar flow in fully developed, pressure driven, channel flow. These flows, generically referred to as transitional, include an instability stage and a nonlinear development stage. The central focus is on the nonlinear development stage. The present analyses use existing direct numerical simulation data sets, as well as recently reported high-resolution molecular tagging velocimetry measurements. Primary considerations stem from the emergence of the effects of turbulent inertia as represented by the Reynolds stress gradient in the mean differential statement of dynamics. The results describe the flow evolution following the formation of a non-zero Reynolds stress peak that is known to first arise near the critical layer of the most unstable disturbance. The positive and negative peaks in the Reynolds stress gradient profile are observed to undergo a relative movement toward both the wall and centreline for subsequent increases in Reynolds number. The Reynolds stress profiles are shown to almost immediately exhibit the same sequence of curvatures that exists in the fully turbulent regime. In the transitional regime, the outer inflection point in this profile physically indicates a localized zone within which the mean dynamics are dominated by inertia. These observations connect to recent theoretical findings for the fully turbulent regime, e.g. as described by Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) and Klewicki, Fife & Wei (J. Fluid Mech., vol. 638, 2009, p. 73). In accord with momentum equation analyses at higher Reynolds number, the present observations provide evidence that a logarithmic mean velocity profile is most rapidly approximated on a sub-domain located between the zero in the Reynolds stress gradient (maximum in the Reynolds stress) and the outer region location of the maximal Reynolds stress gradient (inflection point in the Reynolds stress profile). Overall, the present findings provide evidence that the dynamical processes during the post-laminar regime and those operative in the high Reynolds number regime are connected and describable within a single theoretical framework.

Flow Characteristics around Circular Cylinders with a Normal Slit

2017 ◽  
Vol 379 ◽  
pp. 48-57 ◽  
Author(s):  
Cheng Hsiung Kuo ◽  
Hwa Wei Lin ◽  
Chih Tao Chai ◽  
Fred Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Rear Surface ◽  
Flow Characteristics ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Flow Structures ◽  
Phase Lock ◽  
Layer Flow

Alterations of boundary layer separation along the upper-rear surface of a baseline and slit cylinder and the formation of a vortex in the near-wake are investigated by particle image velocimetry (PIV) at Reynolds number 1000. The slit ratio (S/D) is 0.3. The phase-lock flow structures are referred to the time-dependent volume flux at the slit exit and are achieved by the modified phase-averaged technique. The alterations and the evolution of boundary-layer flow along the upper-rear surface are demonstrated by the phase-lock flow structures. It is found that the alternate blowing and suction at the slit exit serves as a perturbation to the boundary layer near the shoulder of the slit cylinder leading to a significant delay of flow separation and the flow reattachment of boundary-layer flow along the upper-rear surface of the cylinder. After perturbation, the vortex street behind a slit cylinder is more organized and stronger than that behind a baseline cylinder at Reynolds number 1000.

413 Effects of the Orbital Motion on the Boundary Layer Flow over a Rotating Disk under Orbital Motion at High Reynolds Number

2015 ◽  
Vol 2015.68 (0) ◽  
pp. 153-154
Author(s):  
Yasuhiro OKUMURA ◽  
Shinnosuke FUJIKAWA ◽  
Mizue MUNEKATA ◽  
Hiroyuki YOSHIKAWA ◽  
Kazuyuki KUDO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
High Reynolds Number ◽  
Orbital Motion ◽  
Rotating Disk ◽  
Layer Flow ◽  
High Reynolds

Hydroacoustics of Transitional Boundary-Layer Flow

1991 ◽  
Vol 44 (12) ◽  
pp. 517-531 ◽  
Author(s):  
Gerald C. Lauchle
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Pressure Fluctuations ◽  
Local Pressure ◽  
Turbulent Spots ◽  
Layer Flow

Transitional boundary layers exist on surfaces and bodies operating in viscous fluids at speeds such that the critical Reynolds number based on the distance from the leading edge is exceeded. The transition region is composed of a simultaneous mixture of both laminar and turbulent regimes occurring randomly in space and time. The turbulent regimes are known as turbulent spots, they grow rapidly with downstream distance, and they ultimately coalesce to form the beginning of fully-developed turbulent boundary-layer flow. It has been long suspected that such a region of unsteadiness may give rise to local pressure fluctuations and radiated sound that are different from those created by the fully-developed turbulent boundary layer at equivalent Reynolds number. This article reviews the available literature on this subject. The emphasis of this literature is on natural and artificially created transitional boundary layers under mostly incompressible conditions; hence, the word hydroacoustics in the title. The topics covered include the dynamics and local wall pressure fluctuations due to the passage of turbulent spots created in a deterministic way, the pressure fluctuations under transitioning boundary layers where the formation and location of spots are random, and the acoustic radiation from transition and its pre-cursor, the Tollmien-Schlichting waves. The majority of this review is for zero-pressure gradient flat plate flows, but the limited literature on axisymmetric body and plate flows with pressure gradient is included.

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